Answer:
13
Step-by-step explanation:
A trapezoid is a quadrilateral (has four sides and four angles) with two parallel opposite sides. These parallel sides are known as the bases.
According to the mid segment theorem of a trapezoid, The mid segment of a trapezoid is half the lengths of the two parallel sides.
Given that TW is the mid segment, UV and RS are the parallel bases, hence:
[tex]TW=\frac{UV+RS}{2} \\\\-4z+55=\frac{(-z+15)+(-3z+43)}{2} \\\\-4z+55=\frac{-4z+58}{2} \\\\-8z+110=-4z+58\\\\-4z+8z=110-58\\\\4z=52\\\\z=13[/tex]
